Coursework in tomorrow, Completely Stuck

a body mass of 5kg starts off from rest and is acted upon a force of 5N over a distance of 2m. if there is no frictional forces make use of the principle of the conservation of energy to determinei ts final speed

Most of these formulas can be understood quite easily by looking at a velocity-time graph. Since acceleration is constant, velocity will be linear. The slope of the velocity time graph is the acceleration, so rise/run = a = [tex]\frac{v_{f}-v_{i}}{t}[/tex]. Etc. In fact that may be the best way to memorize them.

That's one way to do it, but his question calls for it to be done with conservation of energy equations. Remember that work done by a force is given by multiplying the magnitude of the force by the distance the object moves in the direction of the force:

[tex]
W = Fs
[/tex]

And like turdferguson said, use the work-kinetic energy theorem, which states that the amount of work done is the change in kinetic energy of the system

[tex]
W = \Delta K
[/tex]

and kinetic energy of an object is given by

[tex]
K = \frac{1}{2}m v^2
[/tex]

So, work is done by the 5 N force to increase the kinetic energy of the object. You can find how much work was done, and therefore how much the kinetic energy increased--and therefore how much the velocity increased.